- Chapter 1- Rational and Irrational Numbers
- Chapter 2- Compound Interest [Without Using Formula
- Chapter 3- Compound Interest [Using Formula
- Chapter 4- Expansions
- Chapter 5- Factorisation
- Chapter 6- Simultaneous Equations
- Chapter 7- Indices [exponents]
- Chapter 8- Logarithms
- Chapter 9- Triangles [Congruency in Triangles]
- Chapter 10- Isosceles Triangle
- Chapter 11- Inequalities
- Chapter 12- Mid-Point and Its Converse
- Chapter 13- Pythagoras Theorem
- Chapter 14- Rectilinear Figures
- Chapter 15- Construction of Polygons
- Chapter 16- Area Theorems
- Chapter 17- Circles
- Chapter 18- Statistics
- Chapter 19- Mean and Median
- Chapter 20- Area and Perimeter of Plane Figures
- Chapter 21- Solids
- Chapter 22- Trigonometrical Ratios
- Chapter 23- Trigonometrical Ratios of Standard Angles
- Chapter 24- Solution Of Right Triangles
- Chapter 25- Complementary angles
- Chapter 26- Co-ordinate Geometry
- Chapter 27- Graphical Solution
- Chapter 28- Distance Formula
Selina Solutions Class 9 Mathematics Solutions for Exercise 1(B) in Chapter 1 - Chapter 1- Rational and Irrational Numbers
State whether the following numbers are rational or not:
(i) $(2+\sqrt{2})^{2}$ (ii) $(3-\sqrt{3})^{2}$ (iii) $(5+\sqrt{5})(5-\sqrt{5})$ (iv) $(\sqrt{3}-\sqrt{2})^{2}$ $(\mathbf{v})$ $\left(\frac{3}{2 \sqrt{2}}\right)^{2}$ $(\mathbf{v i})$ $\left(\frac{\sqrt{7}}{6 \sqrt{2}}\right)^{2}$
\begin{aligned} &\text { (i) }\\ &\begin{array}{r} (2+\sqrt{2})^{2}=2^{2}+2(2)(\sqrt{2})+(\sqrt{2})^{2} \\ =4+4 \sqrt{2}+2=6+4 \sqrt{2} \end{array} \end{aligned} ∴, irrational
\begin{aligned} &\text { (ii) }\\ &\begin{aligned} (3-\sqrt{3})^{2}=(3)^{2}-2(3)(\sqrt{3})+(\sqrt{3})^{2} & \\ =9-6 \sqrt{3}+3 \\ =& 12-6 \sqrt{3}=6(2-\sqrt{3}) \end{aligned} \end{aligned} ∴, irrational
\begin{aligned} &\text { (iii) }\\ &\begin{array}{c} (5+\sqrt{5})(5-\sqrt{5})=(5)^{2}-(\sqrt{5})^{2} \\ =25-5=20 \end{array} \end{aligned} ∴, rational
\begin{aligned} &\text { (iv) }\\ &\begin{aligned} (\sqrt{3}-\sqrt{2})^{2}=&(\sqrt{3})^{2}-2(\sqrt{3})(\sqrt{2})+(\sqrt{2})^{2} \\ &=3-2 \sqrt{6}+2=5-2 \sqrt{6} \end{aligned} \end{aligned} ∴, irrational
\begin{aligned} &(\mathrm{v})\\ &\left(\frac{3}{2 \sqrt{2}}\right)^{2}=\frac{(3)^{2}}{(2 \sqrt{2})^{2}}=\frac{9}{4 \times 2}=\frac{9}{8} \end{aligned} ∴, rational
\begin{aligned} &\text { (vi) }\\ &\left(\frac{\sqrt{7}}{6 \sqrt{2}}\right)^{2}=\frac{(\sqrt{7})^{2}}{(6 \sqrt{2})^{2}}=\frac{7}{36 \times 2}=\frac{7}{72} \end{aligned} ∴, rational
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